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HEURISTIC MODELING OF THERMOPHYSICAL PROPERTIES OF PURE FLUIDS AND MIXTURES THROUGH INNOVATIVE METHODS
No full textThe subject of the present Ph.D. thesis is constituted by the development and application of innovative modeling techniques for the representation of the thermophysical properties of fluids.
The thermophysical properties are divided into thermodynamic properties, related to states of thermodynamic equilibrium and to transformation processes between two equilibrium conditions, and transport properties, concerning systems in a non-uniform state and then affected by transport phenomena; among these, thermal conductivity has been here considered.
The knowledge of the thermophysical properties of pure fluids and mixtures is an absolutely crucial need for the design and the optimization of any equipment in the process industry. The thermophysical properties have to be known in dependence on the controlling variables with a precision as high as possible: errors in the values of the required properties can propagate throughout the entire calculation with amplification effects, yielding wrong design and driving away from the optimal operating conditions.
The purpose of this thesis work is to set up modeling techniques able to represent the thermophysical properties with a precision comparable with the experimental uncertainty of the experimental measurements of the properties themselves reducing at the same time the required experimental effort. The proposed modeling techniques are based on a heuristic approach, that get the functional representation of a physical dependence directly from a properly organized data base; the effectiveness of the developed heuristic techniques is fundamentally based on the use of the artificial neural network, which have the characteristic of universal function approximators.
The development and application of a heuristic modeling technique to produce equations of state (EoS) in the fundamental form for the representation of thermodynamic properties of pure fluids and mixture are presented in the first part of this thesis work. The modeling technique here proposed for the representation of the thermodynamic properties is based on the extended corresponding states (ECS) principle. The basic idea of the ECS model consists in the distortion of the independent variables of the EoS of the reference fluid to transform it into the EoS of the interest fluid. If the simple two-parameter corresponding states principle should work exactly, no tuning distortion would be necessary; since this is not the case, two tuning functions, indicated as shape functions, are then individually required to exactly match the ECS model with a known thermodynamic surface of the interest fluid.
The basic requirements of the ECS technique are the fulfillment of a conformality condition between the reference and the target fluid, and the availability of an accurate equation of state in terms of Helmholtz energy for the reference fluid. In the case that either the conformality condition is not verified among the fluids of a same family or no component of the family, whose fluids are supposed to share a conformality condition, disposes of a DEoS, the discussed ECS method cannot in general be effectually applied.
In the model proposed in this thesis the ‘correction’ through the variables distortion is performed on a simple EoS representing, even if roughly, the target fluid itself. In other words a simple EoS for the same target fluid is the starting point for the development of a DEoS through the variables distortion, avoiding in this way any problem about the conformality condition fulfillment. It would be then no more necessary to dispose of a ‘reference fluid’, following the classical interpretation of the ECS theory, but rather of only a ‘reference equation’, whose precision is enhanced, or ‘extended’, through the application of the shape functions. Hence the name of extended equation of state (EEoS) chosen to indicate this new modeling method.
The shape functions have to be regressed forcing the model to represent known values of experimentally accessible thermodynamic quantities; in the present model their functional formulation is heuristically obtained applying a multilayer feed-forward neural network (MLFN) as universal function approximator. The new approach is constituted by a general fitting procedure in which a mathematical form of the surface has to be ‘spread’ on known values of it and of its derivatives, overcoming the problems presented by the two traditional ECS approaches, i.e., the local solution and the continuous solution.
The proposed modeling technique comes from the combination of the EEoS method with the neural networks and then it can be concisely indicated as EEoS-NN model.
The EEoS-NN model allows to obtain for the fluid of interest a DEoS in the default fundamental form which allows to calculate any thermodynamic quantity through mathematical derivations only.
In order to set up the method and to test its potentialities, data generated from a DEoS for each target fluid are used instead of experimental data, so that the model performances are not hindered by error noise and uneven data distribution. Moving from generated data, the capability of the proposed method has been verified both for pure fluids and for mixtures. A group of pure alkanes, haloalkanes, and strongly polar substances has been considered; the results obtained for these fluids are very promising. The same is valid for the five binary mixtures and two ternary mixtures of haloalkanes here studied.
In the case of pure fluids it has been also verified that slightly more than 100 density points evenly distributed in the pressure-density-temperature plane and with low experimental error can be a sufficient input for the model development, allowing to reduce the experimental efforts.
The promising performances for the proposed model based on generated data leads to the possibility to reliably develop DEoSs in the EEoS-NN format directly from experimental data.
The EEoS-NN technique was then applied to draw DEoSs for the pure fluids sulfur hexafluoride (SF6) and 2-propanol (iC3H8O) directly from the available data sets of the target fluids.
The DEoS for SF6 is valid for the liquid, vapor and supercritical region in the ranges from the triple-point temperature at about 223.6 K up to 625 K and for pressures up to 60 MPa, with the exclusion of a region close to the critical point in case of caloric property calculation. The representation of the available experimental data is satisfactory for all the considered properties; in fact the deviations of the equation from the data are comparable with the ascribed uncertainties of the experimental sources. One of the advantages of the EEoS-NN method, shown for the fluid sulfur hexafluoride, is that the data set on which to base the regression procedure can include only density and coexistence values, getting in the meantime a satisfactory performance also for the other properties.
The DEoS for iC3H8O is valid for the liquid, vapor and supercritical region for temperatures from 280 up to 600 K and for pressures up to 50 MPa. Due to the substantial lack of data in the near critical region and the non-specialization of this DEoS in representing such region very close to the critical point the present equation is not suggested to be used within a region very close to the critical point. The representation of the available experimental data is satisfactory for all the considered properties; in fact the deviations of the equation from the data are comparable with the realistic uncertainties of the experimental sources for this fluid. The results obtained for the fluid 2-propanol demonstrate that the EEoS-NN modeling method is completely reliable to develop highly effective DEoSs even if the experimental data situation for the fluid is not completely favorable. This aspect is particularly valuable in the case a DEoS is required for engineering applications where the economy of the experimental effort and the representation accuracy have to be met through a suitable compromise.
The pointed out features make the EEoS-NN technique a useful tool for the process analysis and optimization. To prove the potential of the cited technique as a tool to study real processes typical of the chemical industry the system propylene + 2-propanol + water has been chosen as an exemplification case. The objective is therefore to investigate the possibility to use the EEoS-NN technique to study the energetic optimization of the extraction process of 2-propanol from aqueous solutions using propylene as solvent. This system has been chosen after a screening of the literature data because it seems to present a favorable phase equilibrium behavior for an extraction operation. Furthermore, the propylene + 2-propanol + water system is thermodynamically strongly deviating from ideal behavior due to several causes as the strong polarity of the components, their association behavior, etc., which increases a lot the difficulties of a complete and accurate thermodynamic representation. For such a reason the set up of a DEoS for this system is an interesting challenge from a scientific point of view, being the first case in which a dedicated equation of state is developed for a strongly deviating ternary mixture.
The experimental data available from the literature for the ternary mixture are vapor-liquid equilibrium (VLE) and liquid-liquid equilibrium (LLE). In order to set up a semi-predictive thermodynamic model of the ternary mixture to study its phase behavior, vapor-liquid-liquid equilibrium (VLLE) measurements have been performed. Excess enthalpy measurements have also been carried out for the ternary mixture and for the 2-propanol + water binary mixture in order to obtain a good temperature dependence in the semi-predictive model, constituted of a Peng-Robinson cubic EoS with Wong-Sandler mixing rules and a modified UNIQUAC model to represent the excess Gibbs energy. This model has been used to investigate the phase equilibrium behavior of the ternary mixture from a qualitative point of view. This is a necessary preliminary step to efficiently plan an experimental campaign of measurements suitable to set up a DEoS of the ternary mixture in the EEoS-NN format. The chosen range of interest for the extraction operation is from about 300 to 350 K in temperature, up to 10 MPa in pressure and it extends up to the pure fluids in composition. The properties to be measured in the selected range in order to set up the DEoS are density and phase equilibria. Some isobaric heat capacity measurements are also required to validate the model capability to correctly predict the caloric properties in the range of interest.
Density data have been produced using a vibrating tube densimeter (VTD) for the pure 2-propanol, for the propylene + 2-propanol mixture, for the 2-propanol + water mixture and for the propylene + 2-propanol + water mixture. Bubble pressure data were also determined using the VTD for the propylene + 2-propanol mixture and for the propylene + 2-propanol + water mixture.
At present the experimental work is still in progress and phase equilibrium and isobaric heat capacity data have to be carried out. This experimental work, together with the development of a DEoS for the propylene + 2-propanol + water mixture, will constitute the extension of this thesis work. Once a thermodynamic model in EEoS-NN format will be obtained, it will be possible to link it with a process simulator, studying the better operative conditions for the 2-propanol extraction process.
The development and application of a heuristic modeling technique to produce dedicated equations for the representation of the thermal conductivity of pure fluids is presented in the second part of this thesis work.
The proposed model is based on the ECS principle, but the shape functions are got in a continuous analytical form expressed by a universal function approximator, i.e. a neural network, through regression of thermal conductivity data. This innovative approach, named ECS-NN, allows to overcome the problems in obtaining the scale factors presented by the two traditional ECS approaches for transport properties, i.e., the local solution and the continuous solution. The potentiality of the ECS-NN modeling technique for thermal conductivity has been shown with application to both values generated from existing models and experimental values. Assuming R134a as reference fluid, two dedicated thermal conductivity equations have been regressed for carbon dioxide and R152a from the available experimental data. The obtained results are very encouraging; in fact the proposed technique yields thermal conductivity equations that represent the experimental values in the liquid, vapor and supercritical regions within their experimental accuracy; moreover, the method is able to satisfactorily model the strong critical enhancement of thermal conductivity in the near-critical region.
The performance change of the model has been studied varying the number of experimental data in the training procedure, showing that about two hundred data points, regularly distributed on the thermal conductivity-temperature-density surface of the target fluid, are sufficient to draw a very precise equation, with evident saving of experimental efforts.
Summarizing, the present Ph.D. thesis has shown the effectiveness of the application of heuristic techniques to both thermodynamic and transport property modeling, as a valid alternative to the techniques that are at present adopted. The proposed methods, exploiting the prediction capability of the neural networks, allow to reduce the experimental effort, yielding at the same time equations representing the data within their experimental uncertainties. This feature makes the developed methods suitable tools for the design and optimization of unit operations of the industrial processes.L’argomento di questa tesi di Dottorato è lo sviluppo e l’applicazione di tecniche modellistiche innovative per la rappresentazione di proprietà termofisiche di fluidi.
Le proprietà termofisiche sono divise in proprietà termodinamiche, riguardanti stati di equilibrio termodinamico e processi di trasformazione tra due condizioni di equilibrio, e proprietà di trasporto, riguardanti sistemi in stato non uniforme e quindi caratterizzate da fenomeni di trasporto; tra queste è stata qui trattata la conduttività termica.
La conoscenza delle proprietà termofisiche di fluidi puri e miscele è un requisito assolutamente fondamentale nella progettazione ed ottimizzazione di qualsiasi apparecchiatura nell’industria di processo. Le proprietà termofisiche devono essere conosciute in dipendenza delle variabili controllanti con una precisione il più elevata possibile: errori nel valore delle proprietà richieste possono propagarsi attraverso l’intero calcolo amplificandosi, dando luogo ad una progettazione scorretta ed allontanando dalle condizioni operative ottimali.
Lo scopo di questa tesi è lo sviluppo di tecniche modellistiche capaci di rappresentare le proprietà termofisiche con un’accuratezza comparabile con l’incertezza sperimentale delle misure stesse, riducendo allo stesso tempo il lavoro sperimentale. Le tecniche modellistiche proposte sono basate su un approccio euristico, che deriva la rappresentazione funzionale di una dipendenza fisica direttamente da una appropriata base di dati; l’efficacia delle tecniche euristiche sviluppate è basata sull’utilizzo delle reti neurali artificiali, che hanno la caratteristica di essere approssimatori universali di funzione.
Lo sviluppo e l’applicazione di tecniche modellistiche di natura euristica atte a produrre equazioni di stato (EoS) in forma fondamentale per la rappresentazione delle proprietà termodinamiche di fluidi puri e miscele sono trattati nella prima parte di questa tesi. La tecnica modellistica qui proposta per la rappresentazione delle proprietà termodinamiche è basata sul principio degli stati corrispondenti estesi (ECS). L’idea alla base del modello ECS consiste nella distorsione delle variabili indipendenti della EoS del fluido di riferimento trasformandola nella EoS del fluido di interesse. Se il principio degli stati corrispondenti a due parametri fosse esatto non sarebbero necessari aggiustamenti delle variabili indipendenti, ma poiché questo non è verificato sono richieste due funzioni distorcenti, chiamate shape function, per far corrispondere il modello ECS con una superficie termodinamica nota del fluido d’interesse.
Per l’applicazione della tecnica ECS deve essere verificata la condizione di conformality tra il fluido di riferimento ed il fluido target, e l’esistenza di un’accurata equazione di stato espressa in forma di energia libera di Helmholtz per il fluido di riferimento. Nel caso in cui la condizione di conformality tra i fluidi non sia verificata, o nessun fluido della famiglia che si suppone presenti una condizione di conformality con il fluido di interesse disponga di una DEoS, il metodo ECS non può essere applicato efficacemente.
Nel modello presentato in questa tesi la ‘correzione’ ottenuta attraverso la distorsione delle variabili è applicata ad un’equazione semplice che rappresenta, anche se approssimativamente, lo stesso fluido target. In altre parole, una EoS semplice per il fluido target stesso è il punto di partenza per lo sviluppo di una DEoS per mezzo della distorsione delle variabili, evitando in questo modo il vincolo costituito dalla necessità di soddisfare la condizione di conformality. Non è più quindi necessario disporre di un ‘fluido di riferimento’, come nell’interpretazione classica della teoria ECS, ma piuttosto solo di una ‘equazione di riferimento’, la cui precisione è aumentata, o ‘estesa’, per mezzo dell’applicazione delle shape function. Di qui deriva il nome di extended equation of state (EEoS) scelto per indicare questa nuova tecnica modellistica.
Le shape function devono essere regredite forzando il modello a rappresentare valori noti delle grandezze termodinamiche sperimentalmente accessibili; nel modello proposto la loro forma funzionale è ottenuta in modo euristico utilizzando una multilayer feed-forward neural network (MLFN) come approssimatore universale di funzione. La nuova tecnica è costituita da una procedura di fitting in cui la forma matematica della superficie di deve essere ‘spalmata’ su valori noti della stessa e delle sue derivate, superando i problemi che derivano dai due approcci ECS convenzionali, cioè la local solution e la continuous solution.
La tecnica modellistica proposta deriva dalla combinazione del metodo EEoS con le reti neurali ed è quindi brevemente indicata come EEoS-NN.
Il modello EEoS-NN permette di ottenere per il fluido di interesse una DEoS in forma fondamentale che consente di calcolare ogni proprietà termodinamica attraverso il solo utilizzo di operazioni di derivazione.
Allo scopo di mettere a punto il metodo e di testare le sue potenzialità, sono stati scelti alcuni fluidi target per i quali sono stati utilizzati valori generati da una DEoS preesistente al posto dei dati sperimentali, in modo tale che la performance del modello non sia compromessa dall’error noise e dalla distribuzione irregolare dei dati. Utilizzando dati generati la performance del modello è stata verificata per fluidi puri e per miscele. E’ stato considerato un gruppo di fluidi puri comprendenti alcani, aloalcani, e sostanze fortemente polari; in ogni caso i risultati ottenuti sono molto promettenti. La stessa considerazione può essere fatta per le cinque miscele binarie e le due miscele ternarie di aloalcani studiate.
Nel caso di fluidi puri è stato anche verificato che un numero poco superiore a 100 punti di densità regolarmente distribuiti sul piano pressione-densità-temperatura e caratterizzati da un basso errore sperimentale possono essere un input sufficiente per lo sviluppo del modello, permettendo di ridurre il lavoro sperimentale usualmente necessario per l’ottenimento di una DEoS.
Le promettenti prestazioni ottenute della tecnica modellistica applicata ai dati generati conducono alla possibilità di mettere a punto delle DEoS in forma EEoS-NN utilizzando direttamente dati sperimentali.
La tecnica EEoS-NN è stata quindi utilizzata per produrre la DEoS per i fluidi puri esafluoruro di zolfo (SF6) e 2-propanolo (iC3H8O) direttamente dai dati sperimentali dei due fluidi.
La DEoS per il fluido SF6 è valida nel liquido, vapore e supercritico dalla temperatura del punto triplo, a circa 223.6 K, fino a 625 K e per pressioni fino a 60 MPa, con l’esclusione della regione prossima al punto critico nel caso delle proprietà caloriche. La precisione con cui il modello rappresenta i dati è da considerarsi soddisfacente per tutte le proprietà termodinamiche, infatti le deviazioni dell’equazione dai dati sono confrontabili con l’incertezza attribuita alle fonti sperimentali. Uno dei vantaggi del metodo EEoS-NN, evidenziato nell’applicazione al fluido esafluoruro di zolfo, è che la procedura di regressione della DEoS può essere basata su una base dati comprendente solo valori di densità e coesistenza, ottenendo allo stesso tempo una rappresentazione accurata anche delle altre proprietà.
La DEoS per il fluido iC3H8O è valida nel liquido, vapore e supercritico per temperature da 280 a 600 K e per pressioni fino a 50 MPa. A causa della mancanza di dati nella regione prossima al punto critico e della non-specializzazione della forma funzionale di questa DEoS nella rappresentazione delle proprietà termodinamiche nelle immediate vicinanze del punto critico l’utilizzo della presente equazione è sconsigliato nella suddetta regione. La rappresentazione delle proprietà termodinamiche è soddisfacente per tutte
Thermal conductivity equations of pure fluids in an heuristic extended corresponding states framework. II. Application to two fluids.
No full textThermal conductivity equations of pure fluids in an heuristic extended corresponding states framework. I. Modelling techniques.
No full textA fundamental equation of state for sulfur hexafluoride (SF6) in the extended equation of state format.
No full textAn extended equation of state modeling method. II. Mixtures.
No full textThis work is the extension of previous work dedicated to pure fluids. The same method is extended to the representation of thermodynamic properties of a mixture through a fundamental equation of state in terms of Helmholtz energy. The proposed technique exploits the extended corresponding states concept of distorting the independent variables of a dedicated equation of state for a reference fluid using suitable scale factor functions to adapt the equation to experimental data of a target system. An equation of state for the target mixture is used instead of an equation for the reference fluid, completely avoiding the need for a reference fluid. In particular, a Soave-Redlich-Kwong cubic equation with van der Waals mixing rules is chosen. The scale factors, that are functions of temperature, density, and composition of the target mixture, are expressed in the form of a multilayer feedforward neural network, whose coefficients are regressed by minimizing a suitable objective function involving different kinds of mixture thermodynamic data. As a preliminary test, the model is applied to five binary and two ternary haloalkane mixtures, using data generated from existing dedicated equations of state for the selected mixtures. The results show that the method is robust and straightforward for the effective development of a mixture-specific equation of state directly from experimental data
Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles
No full textThe aim of this paper is the thermodynamic evaluation and optimisation of different two-stage transcritical carbon dioxide cycles. Five different cycles are studied: basic single-stage cycle, single-throttling with two-stage compression cycle, split cycle, phase separation cycle and single-stage cycle coupled with a gas cooling circuit. Each basic cycle is analysed for the effect of internal heat transfer between different streams of refrigerants. In the case of two-stage compression, intermediate cooling between the compressor stages is present. An analysis on the Plank cycle for intermediate pressure higher than critical one is performed. Each cycle is optimised with regards to energy performance, calculating the optimal values of both the upper and the intermediate pressures. In the case of split cycle, the ratio of the mass flow rate in the main stream to the one in the auxiliary stream is also optimised
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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